Abstand zum Mittelpunkt für Hebelaufhängung
About points...
We associate a certain number of points with each exercise.
When you click an exercise into a collection, this number will be taken as points for the exercise, kind of "by default".
But once the exercise is on the collection, you can edit the number of points for the exercise in the collection independently, without any effect on "points by default" as represented by the number here.
That being said... How many "default points" should you associate with an exercise upon creation?
As with difficulty, there is no straight forward and generally accepted way.
But as a guideline, we tend to give as many points by default as there are mathematical steps to do in the exercise.
Again, very vague... But the number should kind of represent the "work" required.
When you click an exercise into a collection, this number will be taken as points for the exercise, kind of "by default".
But once the exercise is on the collection, you can edit the number of points for the exercise in the collection independently, without any effect on "points by default" as represented by the number here.
That being said... How many "default points" should you associate with an exercise upon creation?
As with difficulty, there is no straight forward and generally accepted way.
But as a guideline, we tend to give as many points by default as there are mathematical steps to do in the exercise.
Again, very vague... But the number should kind of represent the "work" required.
About difficulty...
We associate a certain difficulty with each exercise.
When you click an exercise into a collection, this number will be taken as difficulty for the exercise, kind of "by default".
But once the exercise is on the collection, you can edit its difficulty in the collection independently, without any effect on the "difficulty by default" here.
Why we use chess pieces? Well... we like chess, we like playing around with \(\LaTeX\)-fonts, we wanted symbols that need less space than six stars in a table-column... But in your layouts, you are of course free to indicate the difficulty of the exercise the way you want.
That being said... How "difficult" is an exercise? It depends on many factors, like what was being taught etc.
In physics exercises, we try to follow this pattern:
Level 1 - One formula (one you would find in a reference book) is enough to solve the exercise. Example exercise
Level 2 - Two formulas are needed, it's possible to compute an "in-between" solution, i.e. no algebraic equation needed. Example exercise
Level 3 - "Chain-computations" like on level 2, but 3+ calculations. Still, no equations, i.e. you are not forced to solve it in an algebraic manner. Example exercise
Level 4 - Exercise needs to be solved by algebraic equations, not possible to calculate numerical "in-between" results. Example exercise
Level 5 -
Level 6 -
When you click an exercise into a collection, this number will be taken as difficulty for the exercise, kind of "by default".
But once the exercise is on the collection, you can edit its difficulty in the collection independently, without any effect on the "difficulty by default" here.
Why we use chess pieces? Well... we like chess, we like playing around with \(\LaTeX\)-fonts, we wanted symbols that need less space than six stars in a table-column... But in your layouts, you are of course free to indicate the difficulty of the exercise the way you want.
That being said... How "difficult" is an exercise? It depends on many factors, like what was being taught etc.
In physics exercises, we try to follow this pattern:
Level 1 - One formula (one you would find in a reference book) is enough to solve the exercise. Example exercise
Level 2 - Two formulas are needed, it's possible to compute an "in-between" solution, i.e. no algebraic equation needed. Example exercise
Level 3 - "Chain-computations" like on level 2, but 3+ calculations. Still, no equations, i.e. you are not forced to solve it in an algebraic manner. Example exercise
Level 4 - Exercise needs to be solved by algebraic equations, not possible to calculate numerical "in-between" results. Example exercise
Level 5 -
Level 6 -
Question
Solution
Short
Video
\(\LaTeX\)
Need help? Yes, please!
The following quantities appear in the problem:
Länge \(\ell\) / Kraft \(F\) / Drehmoment \(\vec M\) /
The following formulas must be used to solve the exercise:
\(\vec M = \vec \ell \times \vec F \quad \) \(\sum \stackrel{\curvearrowleft}{M} \stackrel{!}{=} \sum \stackrel{\curvearrowright}{M} \quad \)
No explanation / solution video to this exercise has yet been created.
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Visit our YouTube-Channel to see solutions to other exercises.
Don't forget to subscribe to our channel, like the videos and leave comments!
Exercise:
Der unten gezeichnete Hebel sei .m lang und habe g Masse. Wie weit weg von seiner Mitte muss man ihn unterstützen damit er im Gleichgewicht ist? Am Hebel hängen auf der einen Seite die Masse m_.kg und auf der anderen Seite die Masse m_.kg. center tikzpicture filldrawcolorblack fillblack!!white -. rectangle -.; filldrawred -.-.----.---.-.--cycle; drawsnakebrace -.---.-. node midway below ?; drawultra thick .---.; draw -----.; filldrawcolorblack fillblack!!white -.-. rectangle -.-.; draw ---.; filldrawcolorblack fillblack!!white .-. rectangle .-; nodecolorwhite at --. m_; nodecolorwhite at -. m_; tikzpicture center
Solution:
newqtyl.m newqtymhkg newqtyme.kg newqtymz.kg % unknownx % DrehmomentSchritte % PGleichungM_ sscMH + M_ PGleichungF_ell_ sscFH sscellH + F_ell_ PGleichungm_gqtyfracell-uk sscmHg uk + m_gqtyfracell+uk % MGleichungm_g ell-m_guk sscmHg uk + m_g ell+m_guk MGleichungsscmHguk+m_guk + m_guk m_gell -m_gell MGleichungsscmH+m_ + m_guk m_gell -m_gell MGleichunguk fracm_ -m_sscmH+m_+m_ell % PHYSMATH % Man muss den Hebel solqtyxfracm_ -m_sscmH+m_+m_fracellmen-mzn/*mhn+mzn+men*lnm al x xf fracmmzmh+mz+me fracl x xTT vom Mittelpunkt entfernt unterstützen.
Der unten gezeichnete Hebel sei .m lang und habe g Masse. Wie weit weg von seiner Mitte muss man ihn unterstützen damit er im Gleichgewicht ist? Am Hebel hängen auf der einen Seite die Masse m_.kg und auf der anderen Seite die Masse m_.kg. center tikzpicture filldrawcolorblack fillblack!!white -. rectangle -.; filldrawred -.-.----.---.-.--cycle; drawsnakebrace -.---.-. node midway below ?; drawultra thick .---.; draw -----.; filldrawcolorblack fillblack!!white -.-. rectangle -.-.; draw ---.; filldrawcolorblack fillblack!!white .-. rectangle .-; nodecolorwhite at --. m_; nodecolorwhite at -. m_; tikzpicture center
Solution:
newqtyl.m newqtymhkg newqtyme.kg newqtymz.kg % unknownx % DrehmomentSchritte % PGleichungM_ sscMH + M_ PGleichungF_ell_ sscFH sscellH + F_ell_ PGleichungm_gqtyfracell-uk sscmHg uk + m_gqtyfracell+uk % MGleichungm_g ell-m_guk sscmHg uk + m_g ell+m_guk MGleichungsscmHguk+m_guk + m_guk m_gell -m_gell MGleichungsscmH+m_ + m_guk m_gell -m_gell MGleichunguk fracm_ -m_sscmH+m_+m_ell % PHYSMATH % Man muss den Hebel solqtyxfracm_ -m_sscmH+m_+m_fracellmen-mzn/*mhn+mzn+men*lnm al x xf fracmmzmh+mz+me fracl x xTT vom Mittelpunkt entfernt unterstützen.
Meta Information
Exercise:
Der unten gezeichnete Hebel sei .m lang und habe g Masse. Wie weit weg von seiner Mitte muss man ihn unterstützen damit er im Gleichgewicht ist? Am Hebel hängen auf der einen Seite die Masse m_.kg und auf der anderen Seite die Masse m_.kg. center tikzpicture filldrawcolorblack fillblack!!white -. rectangle -.; filldrawred -.-.----.---.-.--cycle; drawsnakebrace -.---.-. node midway below ?; drawultra thick .---.; draw -----.; filldrawcolorblack fillblack!!white -.-. rectangle -.-.; draw ---.; filldrawcolorblack fillblack!!white .-. rectangle .-; nodecolorwhite at --. m_; nodecolorwhite at -. m_; tikzpicture center
Solution:
newqtyl.m newqtymhkg newqtyme.kg newqtymz.kg % unknownx % DrehmomentSchritte % PGleichungM_ sscMH + M_ PGleichungF_ell_ sscFH sscellH + F_ell_ PGleichungm_gqtyfracell-uk sscmHg uk + m_gqtyfracell+uk % MGleichungm_g ell-m_guk sscmHg uk + m_g ell+m_guk MGleichungsscmHguk+m_guk + m_guk m_gell -m_gell MGleichungsscmH+m_ + m_guk m_gell -m_gell MGleichunguk fracm_ -m_sscmH+m_+m_ell % PHYSMATH % Man muss den Hebel solqtyxfracm_ -m_sscmH+m_+m_fracellmen-mzn/*mhn+mzn+men*lnm al x xf fracmmzmh+mz+me fracl x xTT vom Mittelpunkt entfernt unterstützen.
Der unten gezeichnete Hebel sei .m lang und habe g Masse. Wie weit weg von seiner Mitte muss man ihn unterstützen damit er im Gleichgewicht ist? Am Hebel hängen auf der einen Seite die Masse m_.kg und auf der anderen Seite die Masse m_.kg. center tikzpicture filldrawcolorblack fillblack!!white -. rectangle -.; filldrawred -.-.----.---.-.--cycle; drawsnakebrace -.---.-. node midway below ?; drawultra thick .---.; draw -----.; filldrawcolorblack fillblack!!white -.-. rectangle -.-.; draw ---.; filldrawcolorblack fillblack!!white .-. rectangle .-; nodecolorwhite at --. m_; nodecolorwhite at -. m_; tikzpicture center
Solution:
newqtyl.m newqtymhkg newqtyme.kg newqtymz.kg % unknownx % DrehmomentSchritte % PGleichungM_ sscMH + M_ PGleichungF_ell_ sscFH sscellH + F_ell_ PGleichungm_gqtyfracell-uk sscmHg uk + m_gqtyfracell+uk % MGleichungm_g ell-m_guk sscmHg uk + m_g ell+m_guk MGleichungsscmHguk+m_guk + m_guk m_gell -m_gell MGleichungsscmH+m_ + m_guk m_gell -m_gell MGleichunguk fracm_ -m_sscmH+m_+m_ell % PHYSMATH % Man muss den Hebel solqtyxfracm_ -m_sscmH+m_+m_fracellmen-mzn/*mhn+mzn+men*lnm al x xf fracmmzmh+mz+me fracl x xTT vom Mittelpunkt entfernt unterstützen.
Contained in these collections:
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Hebel II by pw
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Holzstab als Hebel by TeXercises
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Wiederholungsaufgaben 2c by ha